Outerplanarity of line graphs and iterated line graphs
نویسندگان
چکیده
منابع مشابه
D-Spectrum and D-Energy of Complements of Iterated Line Graphs of Regular Graphs
The D-eigenvalues {µ1,…,µp} of a graph G are the eigenvalues of its distance matrix D and form its D-spectrum. The D-energy, ED(G) of G is given by ED (G) =∑i=1p |µi|. Two non cospectral graphs with respect to D are said to be D-equi energetic if they have the same D-energy. In this paper we show that if G is an r-regular graph on p vertices with 2r ≤ p - 1, then the complements of iterated lin...
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The line index of a graph G is the smallest k such that the kth iterated line graph of G is nonplanar. We show that the line index of a graph is either infinite or it is at most 4. Moreover, we give a full characterization of all graphs with respect to their line index. © 2007 Elsevier B.V. All rights reserved.
متن کاملConnectivity of iterated line graphs
Let k ≥ 0 be an integer and L(G) be k-th iterated line graph. Niepel, Knor, and Šolteś proved that if G is a 4-connected graph, then κ(L(G)) ≥ 4δ(G) − 6. We prove that the connectivity of G can be relaxed. It is proved that if G is an essentially 4-edge-connected and 3-connected graph, then κ(L(G)) ≥ 4δ(G) − 6. Similar bounds are obtained for essentially 4-edge-connected and 2-connected (1-conn...
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The diameter of a connected graph $G$, denoted by $diam(G)$, is the maximum distance between any pair of vertices of $G$. Let $L(G)$ be the line graph of $G$. We establish necessary and sufficient conditions under which for a given integer $k geq 2$, $diam(L(G)) leq k$.
متن کاملK-ordered Hamiltonicity of Iterated Line Graphs
A graph G of order n is k-ordered hamiltonian, 2 ≤ k ≤ n, if for every sequence v1, v2, . . . , vk of k distinct vertices of G, there exists a hamiltonian cycle that encounters v1, v2, . . . , vk in this order. In this paper, we generalize two well-known theorems of Chartrand on hamiltonicity of iterated line graphs to k-ordered hamiltonicity. We prove that if Ln(G) is k-ordered hamiltonian and...
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ژورنال
عنوان ژورنال: Applied Mathematics Letters
سال: 2011
ISSN: 0893-9659
DOI: 10.1016/j.aml.2011.02.011